To find the distance between the points \((-8, -3)\) and \((-2, -5)\), you can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (-8, -3)\) and \((x_2, y_2) = (-2, -5)\).
Plugging in the coordinates:
\[ d = \sqrt{((-2) - (-8))^2 + ((-5) - (-3))^2} \]
Calculating the differences:
\[ x_2 - x_1 = -2 + 8 = 6 \] \[ y_2 - y_1 = -5 + 3 = -2 \]
Now squaring those differences:
\[ d = \sqrt{(6)^2 + (-2)^2} = \sqrt{36 + 4} = \sqrt{40} \]
Now we simplify \(\sqrt{40}\):
\[ \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10} \]
Next, we can calculate the numeric value of \(2\sqrt{10}\):
\[ \sqrt{10} \approx 3.1623 \quad \text{(approx)} \] \[ 2\sqrt{10} \approx 2 \times 3.1623 \approx 6.3246 \]
Now rounding to the nearest hundredth:
\[ d \approx 6.32 \]
Thus, the distance between the points \((-8, -3)\) and \((-2, -5)\) is approximately \(\boxed{6.32}\).